Tax Effects of Unemployment and the Choice of Educational Type
ABSTRACT This paper examines the effect of taxes on the individuals’ choices of educational direction, and thus on the economy’s skill composition. A proportional labour income tax induces too many workers with high innate ability to choose an educational type with high consumption value and low effort costs. This increases the skill mismatch and aggregate unemployment in the economy. The government can correct for this distortion by use of differentiated tuition fees or tax rates.
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ABSTRACT: How the tax system might affect the individual's educational level is well studied. But the question of how the tax system affects the individual's choice of educational type is mostly ignored. This is an important issue, since the educational choice of today's young generation determines the skill composition of tomorrow's labor force and hence the future production possibilities of the country. This paper studies the problem in a partial model. A progressive tax system might in fact introduce distortions in the individuals's educational choice and induce him to choose more of the educational type with the higher consumption value. If he also puts more weight on the present than on the future, this effect is strengthened further.02/2003;
Article: Tax evasion and occupational choice[show abstract] [hide abstract]
ABSTRACT: This paper is concerned with the combined effect of tax compliance and tax audit policy on the occupational choice of individuals and on public policy objectives such as tax revenue, total production, and social welfare. Individuals are assumed to have a choice between riskless work and a risky entrepreneurial occupation. They are only differentiated according to their attitudes towards risk. More risk averse individuals go into the safe occupation and less risk averse people become entrepreneurs. Tax evasion is only accessible to the latter and therefore its control tends to discourage risk taking. Whether control of tax evasion is desirable for the economy as a whole depends on the objective function of the government. It is shown that tax audit policy has conflicting effects on tax revenue, per capita income, and social welfare. These conflicts are illustrated through a numerical example. In this paper, the emphasis is placed on the clarity and the simplicity of the presentation so as to argue that, even though the tax schedule can hardly be differentiated across individuals, tax evasion and its control can be used by policymakers to introduce variability in the individual's tax treatment.Journal of Public Economics. 02/1991;
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ABSTRACT: A lifetime perspective is appropriate in assessing the welfare implications of government tax policies. Although a number of attempts have been made to ex- amine the excess burden of taxation in life-cycle models, these have tended to ignore the role of human capital accumulation and/or the leisure-income choice. In this paper, we do numerical simulations with a model that takes both of these phenomena into account. We find that under reasonable assumptions, the failure to take into account distortions of human capital decisions produces substantial underestimates of the excess burden of income taxation. In addition, allowing for the endogeneity of human capital increases the efficiency of a personal consumption tax relative to that of an equal yield income tax.International Economic Review 02/1983; 24(3):671-83. · 1.56 Impact Factor
TAX EFFECTS, SEARCH UNEMPLOYMENT, AND
THE CHOICE OF EDUCATIONAL TYPE
CESIFO WORKING PAPER NO. 1622
CATEGORY 1: PUBLIC FINANCE
An electronic version of the paper may be downloaded
• from the SSRN website: www.SSRN.com
• from the CESifo website: www.CESifo-group.de
CESifo Working Paper No. 1622
TAX EFFECTS, SEARCH UNEMPLOYMENT, AND
THE CHOICE OF EDUCATIONAL TYPE
This paper examines the effect of taxes on the individuals’ choices of educational direction,
and thus on the economy’s skill composition. A proportional labour income tax induces too
many workers with high innate ability to choose an educational type with high consumption
value and low effort costs. This increases the skill mismatch and aggregate unemployment in
the economy. The government can correct for this distortion by use of differentiated tuition
fees or tax rates.
JEL Code: J64, J68, H21, H24.
Keywords: unemployment, matching, education, optimal taxation, tuition fees.
P.b. 8131 Dep
Department of Economics
Copenhagen Business School
Department of Economics
Solbjerg Plads 3
November 15, 2005.
This paper has benefited from comments by Rolf Aaberge, John Dagsvik, Erling Holmøy,
Pascalis Raimondos-Møller, Agnar Sandmo, and Knut R. Wangen, as well as conference
participants at the Norwegian-German Seminar on Public Economics in Garmisch-
Partenkirchen, September 2005.
Recently, much attention has been given to the fact that unemployment is
higher for low skilled workers than for highly educated workers. However,
little focus has been given to the fact that di¤erent employment perspectives
exist for di¤erent groups of highly educated workers. As the educational
choice of today’s young generation determines the skill composition and hence
the production possibilities of tomorrow’s labour force, which type of higher
education individuals choose becomes an important issue. The increasing
competition for the location of production to low-cost countries further ac-
tualizes industrialized countries’ focus on high-skilled labor and its compo-
sition. However, although the skill combination is essential for a country’s
economic performance, governments encourage individuals to get higher ed-
ucation while to a great extent ignoring which type of higher education they
This paper examines the link between a country’s tax system and the skill
composition of the work force, and shows that income taxes might increase
the skill mismatch in the society and increase total unemployment. The
presence of labor income taxes induces more high-ability individuals to choose
an educational type with high consumption value. Correspondingly, fewer
high-ability individuals choose to acquire the educational type that requires
more e¤ort than in the absence of taxes.
By introducing the concept of human capital, Schultz (1960) and Becker
(1964) introduced a shift in the economic literature into considering educa-
tion as an investment that yields higher wages later in life. Prior to this,
education was considered a cultural good, and there was emphasis on the
non-pecuniary returns to a job or an education, as seen in Marshall (1920).
The recent literature on the economics of education to a great extent ignores
non-pecuniary returns and costs when modeling the educational decision.
Di¤erent educational directions are associated with di¤erent pecuniary
and non-pecuniary costs and returns. Wage levels vary substantially across
occupations and sectors, as do unemployment rates. The individual’s innate
ability level determines both the e¤ort required to complete a speci…c edu-
cation and the wage return to this particular education. His consumption
value of an educational type depends on the individual speci…c preferences.
The consumption value of education, among other things, consists of the joy
of learning new things, meeting new people, moving to a new city, and en-
joying life as a student, in addition to the increased status in society that
often comes with studying in particular …elds. In addition, education also
brings a consumption value in the future, since it quali…es the individual to
work in his preferred profession. Non-pecuniary returns can be important
motivations for the individual’s educational choice. Alstadsæter (2004) esti-
mates that Norwegian teacher’s college graduates’ willingness to pay for the
consumption value of this educational type was at least 38 % of the present
value of their potential lifetime income. Also, Walker and Zhu (2003) report
a negative wage return to an arts degree in the UK, while the positive wage
return to an engineering degree is substantial. This could mean that art
graduates have a large positive consumption value of this educational type,
such that they are willing to forego earnings by not choosing engineering.
These foregone earnings are then the price on the consumption value of an
arts degree. But it is also possible that the e¤ort costs of completing an
engineering degree would have been so high for the arts major that they for
that reason decide against it.1
In the economic literature, surprisingly little attention has been given to
the question of how the tax system a¤ects the individual’s choice of educa-
tional direction, and even less attention has been given to the consequences
for a country’s skill composition. More work has been done on the e¤ects of
taxes on the level of educational attainment when education is a homogenous
investment alternative; Boskin (1975), Heckman (1976), Dri¢l and Rosen
(1983), and Nielsen and Sørensen (1997).2
Alstadsæter (2003) was the …rst to explicitly analyze the tax e¤ects on
the type of educational attainment, and she argues that a higher wage tax
might induce students to choose more of the educational type with high
consumption value. The model was set in partial equilibrium. Malchow-
Møller and Skaksen (2003) expand the framework set out in Alstadsaeter
(2003). They consider identical workers who decide on on how to allocate
their time between productive and non-productive education and leisure.
They show that it can be optimal to have regressive labour taxation and
high uniform tuition fees.
1As both ability and preferences are important in the educational choice, some individ-
uals with low e¤ort costs when acquiring engineering may also have higher consumption
value from this educational type. These individuals then enjoy both a high wage return
and a high non-pecuniary return to their chosen type of education.
2Much work has also been done on tax e¤ects on occupational choice, in particular
regarding the choice between being an entrepreneur or employee; Pestieu and Possen
(1991), Parker (1996), Bruce (2000), and Gentry and Hubbard (2000).
Also the present paper expands on Alstadsæter (2003) and develops a
simple equilibrium model that captures some important dimensions of the
educational choice when the level of education is given. Education is both
investment and consumption. Individuals with heterogenous ability levels
choose among two educational types. The …rst type yields a positive con-
sumption value, but has long expected unemployment spells and a modest
wage return. The second type yields a higher wage return, shorter expected
unemployment spells, but requires an ability-dependent e¤ort to complete.
Wages are set through wage bargains and unemployment features in equilib-
rium. The wage returns net of taxes and the expected unemployment spells
are thus endogenously determined and are important factors when individu-
als decide on their educational direction.
Proportional income taxes increase the importance of non-pecuniary re-
turns and costs for the choice of educational direction by reducing the im-
portance of expected wage returns. This is because the consumption value
and e¤ort cost are tax exempt returns and costs to education. We show that
taxes distort the individuals’ educational choices, such that too few high-
ability workers choose the educational direction that requires e¤ort, and too
many high-ability workers choose the educational direction associated with
a positive consumption value. This, in turn, implies that too many individ-
uals choose an educational type associate with long expected unemployment
spells. The result is that unemployment is higher than it would have been if
individuals chose the socially optimal educational portfolio. The distortion
can however be corrected for either by imposing higher tuition fees on ed-
ucational types with high consumption values or by subsidizing educational
types that require high e¤ort to complete. Di¤erentiated tax rates can also
be used to correct for this distortion.
The paper is organized as follows. In section 2 the two-sector model
employing two di¤erent educational types is described and we consider the
impact on educational direction and total unemployment from proportional
labour taxation. Section 3 considers welfare, concluding that proportional
taxation distorts the educational decision and thus reduces welfare. The fol-
lowing section evaluates whether di¤erentiated taxes may be used to correct
for this distortion, and we consider the impact of tax di¤erentiation on ed-
ucational direction and total unemployment. In Section 5 we examine the
same issues by extending the model with di¤erentiated tuition fees and sub-
sidies. A discussion is provided in Section 6. Finally we conclude in section
Consider an economy where workers may choose to acquire two di¤erent
types of higher education of the same duration, type c and type e. It is
not necessarily the case that the two types of education provide workers
with di¤erent productivities. However, educational type c brings the worker
a higher consumption value than educational type e. For simplicity and
without loss of generality, we introduce this e¤ect in our model by letting
the consumption value of acquiring education e be zero and the consumption
value of education c be positive. On the other hand, education e is associated
with higher educational e¤ort costs than education c. Again, without loss
of generality, we introduce this e¤ect by letting educational costs associated
with education c be zero and the educational costs associated with sector e
Workers di¤er in ability, a, which is known to the individual and is, with-
out loss of generality, assumed to be uniformly distributed across individuals.
Educational e¤ort costs, ?(a), are decreasing in ability, ?0(a) < 0. That is,
the higher innate ability, the less e¤ort is required in order to attain educa-
tion of type e. The consumption value of type c education is the same for all
individuals.3The choice of educational type is discrete, such that individuals
choose to acquire either education of type c or education of type e.
There are two sectors in the economy, where sector c employs workers
with educational type c and sector e employs workers with educational type
e. The two sectors di¤er in the sense that sector e provides workers with
better employment perspectives. The better employment perspectives both
include high wages and low unemployment probabilities. As both those vari-
ables are endogenously determined in the model, we establish these relative
values by either higher productivity in sector e or lower separation rates from
employment in sector e. This corresponds to higher expected pecuniary pay-
o¤s in sector e; as wages are higher and workers will spend more time in
3Note that we could alternatively assume that workers di¤er with respect to prefer-
ences over the consumption value of education c. With the normalization of letting the
consumption value of educational type e be zero, then a would denote di¤erent preferences
for the consumption value of educational type c. The function ?(a) then captures utility
gain of educational type c where ?0(a) < 0 captures that utility falls with the preference
parameter a. That is, workers with high a have a smaller consumption value of educational
type c than individuals with a low a. The same results as we present in the paper below
would then materialize.
employment during a working life.
We now proceed by setting up a two-sector matching equilibrium model
along the lines of Pissarides (2000) that captures the individual’s educational
decision described above.
2.1Workers and …rms
Unemployed workers search for jobs in sector c or sector e depending on
which type of education they acquire. The matching process in each sector
is captured by a concave, constant-returns-to-scale matching function,
Hj= h(vj;uj);j = c;e;
where Hj is the matching rate, vj is the vacancy rate, and uj is the un-
employment rate. The rates are de…ned as the numbers relatively to the
labour force of the speci…c type. The transition rate into employment for a
worker of type j is given by ?j= Hj=uj= h(?j;1) = ?(?j), where ?j=
captures sectorial labour market tightness. The rate at which vacant jobs
become …lled is qj = Hj=vj = h(1;1=?j) = q (?j). Consequently, we have
?(?j) = ?jq (?j), where ?0(?j) = q (?j)(1 ? ? (?j)) > 0 and q0(?j) < 0.
? 2 (0;1) is the elasticity of the expected duration of a vacancy with respect
to ?j, i.e., ? (?j) = q0(:)?j=q (:). Higher labour market tightness in a sec-
tor, ?j; increases the likelihood of a worker in that sector …nding a job, but
reduces the likelihood for a …rm …nding a worker.
Workers who choose to acquire education of type c enjoy a positive con-
sumption value, where d is the imputed monetary value of this consumption
Let Ucand Ecdenote the expected present values of unemployment and
employment for a worker who has acquired type c education. The value
4As discussed in the introduction, this non-pecuniary returns could include returns
while in education such as the joy of learning new things, meeting new people, moving
to a new city, and enjoying life as a student, but it could also include returns received
after the education is …nished such as status in society, having a fun job etc. Both these
interpretations are valid in our model although we, for simplicity, impute the consumption
value of type c education as a ‡ow value in equations (1) and (2) below. The assumption
enables us to use a model without having workers continuously being born and dying.
Such a model would, however, generate the same qualitative results. The same holds for
the interpretations of the e¤ort costs in equations (3) and (4) below.
functions for a worker i with type c education who is paid wcithen reads:
rEci = R + wci(1 ? t) ? sc(Eci? Uc) + d;
rUc = R + ?c(Ec? Uc) + d;
where r is the discount rate, scis the exogenous separation rate in sector c,
and R is a lump sum transfer that all individuals receive from the government
which re‡ects that the government has some positive revenue requirements.
The parameter t is the proportional income tax. rUcis the average expected
return to an unemployed type c worker’s human capital during job search.
The unemployed worker receives the lump-sum transfer and the consump-
tion value of education. However, the person also has a unit probability of
becoming employed, ?c, and thus to increase his or her value by (Ec? Uc).
Equation (1) can be given a similar interpretation. In addition to the in-
stantaneous returns to employment given by the after tax wage, lump-sum
transfer and the consumption value of education, an employed worker faces
a risk of loosing his or her job, sc, and thus to experience a loss of (Ec?Uc).
Workers who choose to acquire education of type e face e¤ort costs which
depend negatively on their ability. The imputed monetary value of the indi-
vidual e¤ort cost is denoted ?(a), where a is the worker’s ability, a 2 [0;1]
and ?0(a) < 0. Let Ueand Eedenote the expected present values of unem-
ployment and employment. The value functions for a worker with ability a
and type e education who is paid weithen reads:
rEei = R + wei(1 ? t) + se(Uei? Eei) ? ?(a);
rUe = R + ?e(Ee? Ue) ? ?(a);
where seis the exogenous separation rate in sector e. It is straight forward
to interpret these equations in terms of asset equations in a similar fashion
as for type c workers.
Firms opening vacancies in sector j employ workers with the marginal
productivity yj: Their time unit probability of …lling a vacancy is qj. Let Jj
and Vjrepresent the expected present values of an occupied job and a vacant
job for …rms in sector j. The arbitrage equations for a speci…c job paying
the wage wjiand a vacant job in the sector j are:
rJji = yj? wji(1 + z) + sj(Vj? Jji); j = c;e;
= qj(Jj? Vj) ? k; j = c;e;
where z is the payroll tax rate and k denotes vacancy costs. As a …lled job is
an asset owned by the …rm, equation (5) captures the rate of return to this
asset. The rate of return is the instantaneous pro…t made from having this
job being …lled, but the …rms also face a risk of loosing its worker, sj, and
thus to face the loss (Jj? Vj). For a vacant job the rate of return is given
by the vacancy cost, k, but also the unit probability of …nding a worker, qj,
so to …ll this vacancy and make a capital gain of (Jj? Vj).
Individual wages, wciand wei, are determined by individual Nash Bargain-
ing. More speci…cally we solve Maxwji(Eji? Uj)?(Jji? Vj)1??, j = c;e,
where ? denotes the workers’ bargaining power. The …rst order conditions
can be written as ?=(1 ? ?)(1=?)Jj= Ej? Uj, where
? ?1 + z
1 ? t
is the tax wedge, and where we have imposed symmetry and the free entry
condition, Vj= 0, j = c;e.
We can solve for the bargained wage by using this …rst order condition
and equations (1)-(6), assuming free entry, that is Vj= 0, and a symmetric
equilibrium. The bargained wage is given by:
!j= wj(1 + z) = ? (yj+ ?jk); j = c;e;
where !jis the producer wage in sector j. The solution for labour market
tightness in sector j; can be derived from equations (5) and (6), using the
free entry condition and the expression for !j:
k (r + sj)
= (1 ? ?)yj? ??jk; j = c;e:
The sectorial producer wage then follows residually from equation (7).
We assume that ye? ycand sc? sewith a strict inequality in at least one
of the two expressions. From equation (7) and (8) we obtain the result that
labour market tightness and producer wages are higher in sector e, ?e> ?c
and !e> !c. Furthermore, as payroll taxes and income taxes are equal in
the two sectors, then consumer wages, wj must also be higher in sector e
than in sector c, we(1 ? t) > wc(1 ? t).
Steady state unemployment rates for the two types of workers are derived
by considering the ‡ows into and out of unemployment, that is sj(1 ? uj) =
sj+ ?j; j = c;e:
Hence, as a higher labour market tightness in sector e corresponds to
a higher transition rate for workers searching for employment in sector e;
?e> ?c, and sc? se; then the unemployment rate is higher in sector c than
in sector e., i.e., ue< uc.
2.2Education and unemployment
When a worker decides on which type of education to acquire, he or she
compares the value as a type c worker to the value as a type e worker.
The workers could compare the value of unemployment, employment, or a
weighted average of both, of being a type c worker to the equivalent value of
being a type e worker. To simplify the exposition, we will assume that the
discount rate approaches zero. This assumption is of no importance for the
results, but it is convenient as it does not matter whether we compare the
value of unemployment, employment or a weighted average of both, between
the two types of education.
Workers carefully consider the consequences of their choice of educational
direction in a number of dimensions. For example, they compare the expected
unemployment spells of the two types of educations. Moreover, they account
for di¤erences in the after tax wage of the two types of educational directions.
In addition, they account for that type c education is associated with a
positive consumption value whereas education of type e requires e¤ort. As
ability di¤ers across individuals, educational costs associated with type e
education di¤ers. This implies that workers with low ability may …nd it too
costly in terms of e¤ort to acquire education of type e.
The marginal worker has an ability level, ^ a, which makes him or her just
indi¤erent between acquiring education of type c and education of type e. We
can write the condition determining the ability level of the marginal worker
rUc= rUe(^ a):
Using the arbitrage equations, (1)-(4) we can write this condition as
(1 ? uc)wc(1 ? t) + d = (1 ? ue)we(1 ? t) ? ?(^ a);
5Recall that rUj= rEj= ArUj+(1 ? A)rEjwhen the discount rate approaches zero,
for j = c;e and the weight A.
The lower unemployment rate, and the higher take home pay, in sector e
induces individuals to choose type e education rather than type c education.
On the other hand, since type c education holds a direct consumption value
and type e education requires e¤ort, this induces individuals to choose type c
Alternatively to the above approach, we can use equations (2) and (4)
in equation (10) and then the …rst order conditions for Nash Bargaining
following by equation (6) after imposing the free entry condition, Vj= 0;j =
c;e. The condition determining the ability of the marginal worker may then
be written as
?(^ a) =
1 ? ?
?(?e? ?c) ? d:
This equation gives ^ a as a function of the endogenous variables ?cand ?e.
As ?cand ?eare determined in equation (8), where ?e? ?c> 0, ^ a and 1 ? ^ a
resolve the number of workers acquiring type c education and the number
of workers acquiring education of type e. Workers with a ? ^ a; choose to
acquire education of type c whereas workers with a > ^ a acquire education
of type e. From equation (12) it is clear that the individual’s choice of
educational type is independent of whether taxes are levied on …rms or on
workers. Any reallocation of the tax burden across the individual and the
…rm is counteracted by adjustments in the pre-tax wage set in the bargains.
Conducting comparative statics on the allocation of workers across the
two types of education reveals that:
Proposition 1 Increased taxation induces some workers to reallocate their
choice of educational direction from type e towards type c, that is @^ a=@? > 0.
Proof. Di¤erentiating equation (12) with respect to ^ a and ? gives the result
immediately as ?j;j = c;e are una¤ected by a change in ? and ?0(^ a) < 0.
Higher income taxes reduce the monetary return to both educational
types, while both the consumption value of type c education and the e¤ort
cost of type e education are unchanged. As the monetary return to the edu-
cational types are reduced through the increased tax, non-monetary returns
become more important for the educational decision. It thus follows intu-
itively that some workers will reallocate their choice of educational direction
towards the type of education which is associated with a positive consump-
tion value and away from the type of education which is associated with
e¤ort costs. It is simply no longer worth while for these individual’s to ac-
quire type e education as the expected net of taxes wage premium no longer
fully compensates their e¤ort costs.
Total unemployment is given by
UTOT= ^ auc+ (1 ? ^ a)ue:
We have the following result.
Proposition 2 Increased taxation raises total unemployment, @UTOT=@? >
Proof. Di¤erentiating equation (13) with respect to ? gives @UTOT=@? =
^ a(uc? ue)@^ a=@?. Hence the result follows from proposition (1) and using
that uc> ue.
Total unemployment increases with higher tax rates simply because more
people choose to acquire education of type c where the unemployment rate
is higher. Lower tax rates will thus reduce total unemployment as it encour-
ages workers to choose an educational type associated with shorter expected
This section is concerned with welfare analysis. We make use of a utilitar-
ian welfare function, which is obtained by adding all individuals’ and …rms’
steady state ‡ow values of welfare. The social welfare function is written as:
SW = ^ a~ Wc+
~ Wc = ucrUc+ (1 ? uc)rEc+ (1 ? uc)rJc+ vcrVc;
~ We = uerUe+ (1 ? ue)rEe+ (1 ? ue)rJe+ verVe:
The government budget restriction is
[^ a(1 ? uc)wc+ (1 ? ^ a)(1 ? ue)we](t + z) = R; which can be written in terms
of producer wages as:
[^ a(1 ? uc)!c+ (1 ? ^ a)(1 ? ue)!e](1 ? 1=?) = R:
By making use of the asset equations for workers and …rms in the two
sectors, equations (1)-(6), imposing the ‡ow equilibrium conditions,6as well
as the government budget restriction in (17), and considering the case of no
discounting, i.e., r ! 0, we can write the welfare function as follows:
SW = Wc^ a +
Wc = (1 ? uc)yc? uc?ck + d;
We = (1 ? ue)ye? ue?ek ? ?(a).
Welfare increases in employment and productivity and decreases in va-
cancy costs. Furthermore, the consumption value tends to increase welfare
whereas educational costs tend to reduce welfare. With the assumption of
risk neutral individuals, we ignore distributional issues and hence wages will
not feature in the welfare function.
As is clear from (18), (19), and (20), the proportional tax rate can only
a¤ect welfare through its impact on the allocation of workers across the two
educational types. The following condition determines the optimal allocation
of workers across the two types of education:
@ (1 ? ^ a)= We(^ a?)?Wc= (1 ? ue)!e??(^ a?)?(1 ? uc)!c?d = 0; (21)
where ^ a?denotes the socially optimal educational allocation. Welfare raises
when more workers acquire education of type e whenever the number of
workers with educational direction e are too low from a welfare point of
view. Similarly, welfare falls as more workers acquire education of type e
when too many workers have education of type e from a welfare perspective.
This clearly follows by de…nition as SW is concave in (1?^ a) and reaches its
maximum when (1 ? ue)!e? ?(^ a?) ? (1 ? uc)!c? d = 0.
Comparing this socially optimal allocation of workers across the two edu-
cational types, equation (21), to the market solution given by equation (12)
gives the following result.
Proposition 3 The presence of taxation, i.e., ? > 1, induces too many
workers to choose educational type c, and thus too few workers to choose
6Flow equilibrium implies sj(1 ? uj) = ?jujand qjvj= sj(1 ? uj).
educational type e. Only when there are no taxation, i.e., ? = 1; will the pri-
vate allocation of workers across the two educational types equal the socially
Proof. The equation for the private solution for the educational direction,
(11) can be written as ((1 ? ue)!e? (1 ? uc)!c)=? ? ?(^ a) ? d = 0 by us-
ing that wj(1 ? t) = !j=?.
@SW=@ (1 ? ^ a) > 0, that is, increasing 1 ? ^ a, would increase welfare. Only
when there are no taxation, i.e., ? = 1; will the private allocation of workers
across the two educational types equal the socially optimal allocation, i.e.,
^ a = ^ a?.
By comparing the equation for the market allocation of workers across
the two types, it is clear that the proportional tax system distorts the in-
dividuals’ educational choices. Too few workers will choose the educational
direction which is associated with e¤ort and too many workers will choose
the educational direction which is associated with a positive consumption
When the government has a positive revenue requirement, R > 0, and
the government can only attain these with proportional tax rates, those
should be chosen as low as possible on order to minimize the distortion
in the educational allocation. Thus the tax rates should be set such that:
(t + z) = R=[^ a(1 ? uc)wc+ (1 ? ^ a)(1 ? ue)we]. The higher the government
revenue requirement, the higher the tax rates and the more ine¢cient will
the educational allocation be, and the lower will welfare be. See the appendix
for the formal set-up of the welfare maximization problem.
The ine¢ciently low number of workers that choose education of type
e in the private solution in presence of proportional uniform taxation could
however be corrected by the use of other policy instruments. Potential policy
instruments are sector speci…c payroll tax rates, di¤erentiated tuition fees and
subsidies. These policy instruments are considered in turn in the following
For ? > 1; the private solution of ^ a induces
4Di¤erentiated tax rates
In this section we consider the option of using di¤erentiated tax rates instead
of a uniform income tax. That is, we may have that the tax wedges are dif-
ferent in sector c and e, denoted as ?c6= ?edue to either tc6= teor zc6=
zeor both. Introducing sector speci…c proportional taxation implies that we
allow the tax rates in the value functions to di¤er. The equilibrium expres-
sions derived from the …rst order condition from the wage bargains now take
the form (?=(1 ? ?))Jj=?j= Ej? Ujwhere ?j= (1 + zj)=(1 ? tj): As we
know from standard theory of imperfectly competitive labour markets, pro-
portional tax rates will not in‡uence producer wages and the unemployment
rate.7This holds also here, inducing that equations (7), (8) and (9) again
pin down the producer wage, tightness, and the unemployment rate for each
of the two sectors depending on the same exact parameter speci…cation.
However, the consumer wages are a¤ected by the tax rates, wj(1 ? tj) =
!j=?j; which implies that also the allocation of workers across the two edu-
cational directions is a¤ected. We can now write the equation determining
the educational allocation as:
Hence, changes in the sector speci…c tax rates a¤ect the allocation of
workers across the education types. We can summarize the impact of di¤er-
entiated taxation on the allocation of workers and on total unemployment in
the following proposition
?(^ a) =
1 ? ?k?e
Proposition 4 An increase in the taxation of workers in sector c, i.e., a
higher ?c; or a reduction in the taxation of workers in sector e, i.e., a lower
?e, induces less individuals to choose education of type c and more individuals
to choose education of type e. The total number of unemployed workers fall.
Proof. As ?cand ?eare determined by (8) independently of the tax rates,
we can from equation (22) derive @^ a=@?c< 0 and @^ a=@?e> 0.
ferentiating equation (13) with respect to ?cand ?e, respectively, gives
= (uc? ue)@^ a
Increasing the relative taxation on workers with an education associated
with a positive consumption value makes it less attractive to choose this
type of education. Some workers thus …nd it optimal to reallocate their
educational choice towards the educational type e; although this educational
type is associated with e¤ort costs. As a larger fraction of the work force
choose an education which is associated with shorter expected unemployment
spells, total unemployment falls.
= (uc? ue)
7See, for example, Pissarides 1998.